Combinatorics and their evolution in resolution of embedded algebroid surfaces

The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object evolves through the resolution of singularities is not really w...

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Detalles Bibliográficos
Autores: Cobo Pablos, M. Helena, Soto Prieto, Manuel Jesús, Tornero Sánchez, José María
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/166463
Acceso en línea:https://hdl.handle.net/11441/166463
https://doi.org/10.18550/arXiv.1905.12338
Access Level:acceso abierto
Palabra clave:Resolution of surface singularities
Newton polygon
Equimultiple locus
Blowing-up
Descripción
Sumario:The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object evolves through the resolution of singularities is not really well understood, as some references had pointed out. The aim of this paper is to study how this object changes as the surface gets resolved. In order to get a precise description of the phenomena involved, we need to use different techniques and ideas. Eventually, some effective results regarding the number of blow-ups needed to decrease the multiplicity are obtained as a side product.